Scalar gradient fields by geometric measure theory
نویسندگان
چکیده
منابع مشابه
Geometric Measure Theory
The aim of these pages is to give a brief, self-contained introduction to that part of Geometric Measure Theory which is more directly related to the Calculus of Variations, namely the theory of currents and its applications to the solution of Plateau problem. (The theory of finite perimeter sets, which is closely related to currents and to the Plateau problem, is treated in the article “Free i...
متن کاملPerturbation Theory and Non-Renormalizable Scalar Fields
We study how to set up systematic summation rules that could permit us to interpret the divergent expressions arising in the perturbation theory of : P(φ) :d when one does not allow any renormalization besides the usual coupling constants, mass and wave function renormalizations.
متن کاملProbability Distributions for Gradient Directions in Uncertain 3D Scalar Fields
This report introduces a mathematical framework to compute probability density functions for the directions of gradients in Gaussian distributed uncertain 3D scalar fields, and illustrates results by means of several examples.
متن کاملDiscrete methods in geometric measure theory
The thesis addresses problems from the field of geometric measure theory. It turns outthat discrete methods can be used efficiently to solve these problems. Let us summarizethe main results of the thesis.In Chapter 2 we investigate the following question proposed by Tamás Keleti. Howlarge (in terms of Hausdorff dimension) can a compact set A ⊂ R be if it does notcontain some...
متن کاملA Basic Introduction of Geometric Measure Theory
Geometric measure theory studies properties of measures, functions and sets. In this note, we provide a basic introduction of geometric measure theory. We will study elementary properties of Hausdorff measures, Lipschitz functions and countably rectifiable sets. To make this note easily accessible, we confine our discussions in Euclidean spaces. Important topics include the area and coarea form...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review E
سال: 2004
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.69.047301